Current literature show that frequency diverse arrays (FDAs) are able of producing range-angle-dependent and time-variant transmit beampatterns, but the resulting time and range dependencies and their characteristics are still not well understood. This paper examines the FDA transmission model and the model for the FDA array factor, considering their time-range relationship. We develop two FDA transmit beampatterns, both yielding the auto-scanning capability of the FDA transmit beams. The scan speed, scan volume, and initial mainlobe direction of the beams are also analyzed. In addition, the equivalent conditions for the FDA integral transmit beampattern and the multiple-input multiple-output (MIMO) beampattern are investigated. Various numerical simulations illustrate the auto-scanning property of the FDA beampattern and the proposed equivalent relationship with the MIMO beampattern, providing the basis for an improved understanding and design of the FDA transmit beampattern.

31 pages, 9 figures